An elastic band is made of a polymer, which is a material that is composed of...

 

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An elastic band is made of a polymer, which is a material that is composed of single units, called monomers, connected to each other like the links of a chain. An overly simplified microscopic model of this is a one-dimensional chain of N links, each of length , where each link can be aligned forward or backward. This means the microstate of the band can be fully given by the number of links aligned forward N+ (or equivalently, the number of links aligned backward N = N-N+). Let us call the the macroscopic length of the band, the distance from the beginning to the end, L. (a) Using the first and second laws, show that the tension of the band is given by f = -T as ƏL where S= S(T, L). (b) Using the linked chain model above, find an expression for f in terms of the thermodynamic quantities and l. An elastic band is made of a polymer, which is a material that is composed of single units, called monomers, connected to each other like the links of a chain. An overly simplified microscopic model of this is a one-dimensional chain of N links, each of length , where each link can be aligned forward or backward. This means the microstate of the band can be fully given by the number of links aligned forward N+ (or equivalently, the number of links aligned backward N = N-N+). Let us call the the macroscopic length of the band, the distance from the beginning to the end, L. (a) Using the first and second laws, show that the tension of the band is given by f = -T as ƏL where S= S(T, L). (b) Using the linked chain model above, find an expression for f in terms of the thermodynamic quantities and l.